What is the integral from pi/2 to pi of 3sin(x) ?

The integral from pi/2 to pi of 3sin(x) is 3

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integral from pi/2 to pi of 3sin(x)

\int_{\frac{π}{2}}^{π} 3 sin (x) d x

3

Solution steps

\int_{\frac{π}{2}}^{π} 3 sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{\frac{π}{2}}^{π} sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= 3 [- cos (x)]_{\frac{π}{2}}^{π}

Compute the boundaries:

1

= 3 \cdot 1

Simplify

= 3

\int_{0}^{\frac{y}{3}} (\frac{y ^{2} - 9 x ^{2}}{2}) d x

\int_{1}^{8} - \frac{1}{8} x + 1 d x

\int_{0}^{x} 9 - t^{2} d t

\int_{0}^{x} 40 e^{- 5 x - 3 y} d y

\int_{- 1}^{1} (1 + x^{2})^{2} d x

What is the integral from pi/2 to pi of 3sin(x) ?
The integral from pi/2 to pi of 3sin(x) is 3